1. Field of the Invention
This invention relates to sensing the position of an object placed within a living body. More particularly, this invention relates to improvements in a catheter tracking system.
2. Description of the Related Art
The meanings of certain acronyms and abbreviations used herein are given in Table 1.
TABLE 1Acronyms and AbbreviationsFERFluoroscopic Effect. ReductionLAOLeft. Anterior-ObliqueLPLocation PadRAORight Anterior-ObliqueSIDSource-to-Image Distance
A wide range of medical procedures involve placing objects, such as sensors, tubes, catheters, dispensing devices, and implants, within the body. Real-time imaging methods are often used to assist doctors in visualizing the object and its surroundings during these procedures. Some methods track the objects using the object using magnetic fields. However, disturbances in the magnetic field may create tracking errors.
Catheters are frequently inserted into patients while using an x-ray fluoroscope to monitor the process in conjunction with a magnetic tracking system. During the procedure, the fluoroscope may be activated as an extra visual check on anatomic maps that may be available or concurrently produced, and in order to view other instruments that may be internally situated within a patient. To that end operators prefer to place the detector as close to the patient as possible. This minimizes the radiation dose to the staff and maximizes the size of the projected images. However, when the fluoroscope detector is placed too near to the patient, its metallic components distort the magnetic field measurements, which are essential to the magnetic tracking system. The distortion causes the magnetic tracking system to report apparent location and orientation shifts from their true values. Translational shifts can reach several centimeters, and rotational shifts can be as large as several degrees. Such shifts could or cause the operator to lose confidence in the magnetic tracking system or even mislead an operator who was unaware of the distortion.
U.S. Pat. No. 6,147,480, to Osadchy et al., whose disclosure is incorporated herein by reference, describes a method for tracking an object using energy fields in the presence of interference due to introduction of an article responsive to the fields, and in the vicinity of the object.
U.S. Patent Application Publication No. 2012/0165656 to Montag et al., which is commonly assigned and herein incorporated by reference, describes generating, using a plurality of magnetic transmitters, a magnetic field in a region and introducing a field-perturbing element into the region. The method includes characterizing multiple images of each magnetic transmitter in the field-perturbing element, and calculating a reaction magnetic field in the region based on the characterized images. The method further includes positioning a probe in the region and measuring a perturbed magnetic field at the probe, and determining a location of the probe in response to the measured perturbed magnetic field and the calculated reaction magnetic field. The method described in U.S. Patent Application Publication No. 2012/0165656 is based on a spatial transfer matrix as set forth in paragraphs and FIGS. 8A to 8G of this reference.
An example of the spatial transfer matrix in U.S. Patent Application Publication No. 2012/0165656 is Tspatial(x,y,z). As described in U.S. Patent Application Publication No. 2012/0165656, Tspatial(x,y,z) is a 3×15 spatial transfer matrix that is derived from spherical harmonic terms, and is calculated from the following exemplary equations A-O as set forth in FIGS. 8A to 8G of this reference and outlined below:
                                                                        3                π                                      ⁢            xz                                2            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            5                /                2                                                    ⁢                                  ⁢                                                                              3                  π                                            ⁢              yz                                      2              ⁢                                                (                                                            x                      2                                        +                                          y                      2                                        +                                          z                      2                                                        )                                                  5                  /                  2                                                              ⁢                                          -                                                    x                2                            +                              y                2                            -                              2                ⁢                                  z                  2                                                                    2              ⁢                                                3                  ⁢                  π                                            ⁢                                                (                                                            x                      2                                        +                                          y                      2                                        +                                          z                      2                                                        )                                                  5                  /                  2                                                                                        Equation        ⁢                                  ⁢        A        ⁢                                  ⁢                  -                ⁢                                  ⁢        Column        ⁢                                  ⁢        1                                                                                    -                2                            ⁢                              x                2                                      +                          y              2                        +                          z              2                                            2            ⁢                                          6                ⁢                π                                      ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            5                /                2                                                    ⁢                                  -                                                            3                                  2                  ⁢                  π                                                      ⁢            xy                                2            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            5                /                2                                                    ⁢                                  -                                                            3                                  2                  ⁢                  π                                                      ⁢            xz                                2            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            5                /                2                                                                        Equation        ⁢                                  ⁢        B        ⁢                                  ⁢                  -                ⁢                                  ⁢        Column        ⁢                                  ⁢        2                                          -                                                                      3                                      2                    ⁢                    π                                                              ⁢              xy                                      2              ⁢                                                (                                                            x                      2                                        +                                          y                      2                                        +                                          z                      2                                                        )                                                  5                  /                  2                                                                    ⁢                                  ⁢                                                            x                2                            -                              2                ⁢                                  y                  2                                            +                              z                2                                                    2              ⁢                                                6                  ⁢                  π                                            ⁢                                                (                                                            x                      2                                        +                                          y                      2                                        +                                          z                      2                                                        )                                                  5                  /                  2                                                              ⁢                                          -                                                                      3                                      2                    ⁢                    π                                                              ⁢              yz                                      2              ⁢                                                (                                                            x                      2                                        +                                          y                      2                                        +                                          z                      2                                                        )                                                  5                  /                  2                                                                                        Equation        ⁢                                  ⁢        C        ⁢                                  ⁢                  -                ⁢                                  ⁢        Column        ⁢                                  ⁢        3                                                      -                                          3                ⁢                                  x                  ⁡                                      (                                                                  x                        2                                            +                                              y                        2                                            -                                              4                        ⁢                                                  z                          2                                                                                      )                                                                              4                ⁢                                                      5                    ⁢                    π                                                  ⁢                                                      (                                                                  x                        2                                            +                                              y                        2                                            +                                              z                        2                                                              )                                                        7                    /                    2                                                                                ⁢                                          -                                    3              ⁢                              y                ⁡                                  (                                                            x                      2                                        +                                          y                      2                                        -                                          4                      ⁢                                              z                        2                                                                              )                                                                    4              ⁢                                                5                  ⁢                  π                                            ⁢                                                (                                                            x                      2                                        +                                          y                      2                                        +                                          z                      2                                                        )                                                  7                  /                  2                                                                    ⁢                                  ⁢                                            6              ⁢                              z                3                                      -                          9              ⁢                              (                                                      x                    2                                    +                                      y                    2                                                  )                            ⁢              z                                            4            ⁢                                          5                ⁢                π                                      ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            7                /                2                                                                        Equation        ⁢                                  ⁢        D        ⁢                                  ⁢                  -                ⁢                                  ⁢        Column        ⁢                                  ⁢        4                                                                                                      3                                      10                    ⁢                    π                                                              ⁢                              z                ⁡                                  (                                                                                    -                        4                                            ⁢                                              x                        2                                                              +                                          y                      2                                        +                                          z                      2                                                        )                                                                    2              ⁢                                                (                                                            x                      2                                        +                                          y                      2                                        +                                          z                      2                                                        )                                                  7                  /                  2                                                              ⁢                                          -                                                                      15                                      2                    ⁢                    π                                                              ⁢              xyz                                      2              ⁢                                                (                                                            x                      2                                        +                                          y                      2                                        +                                          z                      2                                                        )                                                  7                  /                  2                                                                    ⁢                                  ⁢                                                            3                                  10                  ⁢                  π                                                      ⁢                          x              ⁡                              (                                                      x                    2                                    +                                      y                    2                                    -                                      4                    ⁢                                          z                      2                                                                      )                                                          2            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            7                /                2                                                                        Equation        ⁢                                  ⁢        E        ⁢                                  ⁢                  -                ⁢                                  ⁢        Column        ⁢                                  ⁢        5                                                      -                                                                                3                                          10                      ⁢                      π                                                                      ⁢                                  y                  ⁡                                      (                                                                                            -                          4                                                ⁢                                                  x                          2                                                                    +                                              y                        2                                            +                                              z                        2                                                              )                                                                              2                ⁢                                                      (                                                                  x                        2                                            +                                              y                        2                                            +                                              z                        2                                                              )                                                        7                    /                    2                                                                                ⁢                                          -                                                                      3                                      10                    ⁢                    π                                                              ⁢                              x                ⁡                                  (                                                            x                      2                                        -                                          4                      ⁢                                              y                        2                                                              +                                          z                      2                                                        )                                                                    2              ⁢                                                (                                                            x                      2                                        +                                          y                      2                                        +                                          z                      2                                                        )                                                  7                  /                  2                                                                    ⁢                                  ⁢                                                            15                                  2                  ⁢                  π                                                      ⁢            xyz                                2            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            7                /                2                                                                        Equation        ⁢                                  ⁢        F        ⁢                                  ⁢                  -                ⁢                                  ⁢        Column        ⁢                                  ⁢        6                                          -                                                                      15                                      2                    ⁢                    π                                                              ⁢              xyz                                      2              ⁢                                                (                                                            x                      2                                        +                                          y                      2                                        +                                          z                      2                                                        )                                                  7                  /                  2                                                                    ⁢                                  ⁢                                                            3                                  10                  ⁢                  π                                                      ⁢                          z              ⁡                              (                                                      x                    2                                    -                                      4                    ⁢                                          y                      2                                                        +                                      z                    2                                                  )                                                          2            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            7                /                2                                                    ⁢                                  ⁢                                                            3                                  10                  ⁢                  π                                                      ⁢                          y              ⁡                              (                                                      x                    2                                    +                                      y                    2                                    -                                      4                    ⁢                                          z                      2                                                                      )                                                          2            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            7                /                2                                                                        Equation        ⁢                                  ⁢        G        ⁢                                  ⁢                  -                ⁢                                  ⁢        Column        ⁢                                  ⁢        7                                                      -                                                                                3                                          10                      ⁢                      π                                                                      ⁢                                  y                  ⁡                                      (                                                                                            -                          4                                                ⁢                                                  x                          2                                                                    +                                              y                        2                                            +                                              z                        2                                                              )                                                                              2                ⁢                                                      (                                                                  x                        2                                            +                                              y                        2                                            +                                              z                        2                                                              )                                                        7                    /                    2                                                                                ⁢                                          -                                                                      3                                      10                    ⁢                    π                                                              ⁢                              x                ⁡                                  (                                                            x                      2                                        -                                          4                      ⁢                                              y                        2                                                              +                                          z                      2                                                        )                                                                    2              ⁢                                                (                                                            x                      2                                        +                                          y                      2                                        +                                          z                      2                                                        )                                                  7                  /                  2                                                                    ⁢                                  ⁢                                                            15                                  2                  ⁢                  π                                                      ⁢            xyz                                2            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            7                /                2                                                                        Equation        ⁢                                  ⁢        H        ⁢                                  ⁢                  -                ⁢                                  ⁢        Column        ⁢                                  ⁢        8                                                      5            ⁢                          xz              ⁡                              (                                                      4                    ⁢                                          z                      2                                                        -                                      3                    ⁢                                          (                                                                        x                          2                                                +                                                  y                          2                                                                    )                                                                      )                                                          4            ⁢                                          7                ⁢                π                                      ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                    ⁢                                  ⁢                              5            ⁢                          yz              ⁡                              (                                                      4                    ⁢                                          z                      2                                                        -                                      3                    ⁢                                          (                                                                        x                          2                                                +                                                  y                          2                                                                    )                                                                      )                                                          4            ⁢                                          7                ⁢                π                                      ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                    ⁢                                  ⁢                                            8              ⁢                              z                4                                      -                          24              ⁢                              (                                                      x                    2                                    +                                      y                    2                                                  )                            ⁢                              z                2                                      +                          3              ⁢                                                (                                                            x                      2                                        +                                          y                      2                                                        )                                2                                                          4            ⁢                                          7                ⁢                π                                      ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                                        Equation        ⁢                                  ⁢        I        ⁢                                  ⁢                  -                ⁢                                  ⁢        Column        ⁢                                  ⁢        9                                                                                                                                                3                                              7                        ⁢                        π                                                                              ⁢                                      (                                                                  4                        ⁢                                                  x                          4                                                                    +                                              3                        ⁢                                                  (                                                                                    y                              2                                                        -                                                          9                              ⁢                                                              z                                2                                                                                                              )                                                ⁢                                                  x                          2                                                                    -                                                                                                                                                                                      y                      4                                        +                                          4                      ⁢                                              z                        4                                                              +                                          3                      ⁢                                              y                        2                                            ⁢                                              z                        2                                                                              )                                                                          8            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                    ⁢                                  ⁢                              5            ⁢                                          3                                  7                  ⁢                  π                                                      ⁢                          xy              ⁡                              (                                                      x                    2                                    +                                      y                    2                                    -                                      6                    ⁢                                          z                      2                                                                      )                                                          8            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                    ⁢                                  ⁢                              5            ⁢                                          3                                  7                  ⁢                  π                                                      ⁢                          xz              ⁡                              (                                                      3                    ⁢                                          (                                                                        x                          2                                                +                                                  y                          2                                                                    )                                                        -                                      4                    ⁢                                          z                      2                                                                      )                                                          8            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                                        Equation        ⁢                                  ⁢        J        ⁢                                  ⁢                  -                ⁢                                  ⁢        Column        ⁢                                  ⁢        10                                                                                    15                                  14                  ⁢                  π                                                      ⁢                          xz              ⁡                              (                                                      5                    ⁢                                          x                      2                                                        -                                      9                    ⁢                                          y                      2                                                        -                                      2                    ⁢                                          z                      2                                                                      )                                                          4            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                    ⁢                                  ⁢                                                                              15                                      14                    ⁢                    π                                                              ⁢                              yz                ⁡                                  (                                                            9                      ⁢                                              x                        2                                                              -                                          5                      ⁢                                              y                        2                                                              +                                          2                      ⁢                                              z                        2                                                                              )                                                                    4              ⁢                                                (                                                            x                      2                                        +                                          y                      2                                        +                                          z                      2                                                        )                                                  9                  /                  2                                                              ⁢                                          -                                                                      15                                      14                    ⁢                    π                                                              ⁢                              (                                  x                  -                  y                                )                            ⁢                              (                                  x                  +                  y                                )                            ⁢                              (                                                      x                    2                                    +                                      y                    2                                    -                                      6                    ⁢                                          z                      2                                                                      )                                                    4              ⁢                                                (                                                            x                      2                                        +                                          y                      2                                        +                                          z                      2                                                        )                                                  9                  /                  2                                                                                        Equation        ⁢                                  ⁢        K        ⁢                                  ⁢                  -                ⁢                                  ⁢        Column        ⁢                                  ⁢        11                                                                                                                                                5                                              7                        ⁢                        π                                                                              ⁢                                      (                                                                                            -                          4                                                ⁢                                                  x                          4                                                                    +                                              3                        ⁢                                                  (                                                                                    7                              ⁢                                                              y                                2                                                                                      +                                                          z                              2                                                                                )                                                ⁢                                                  x                          2                                                                    -                                                                                                                                                                3                    ⁢                                                                  y                        2                                            ⁡                                              (                                                                              y                            2                                                    +                                                      z                            2                                                                          )                                                                              )                                                                          8            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                    ⁢                                  -                                                            5                                  7                  ⁢                  π                                                      ⁢                          xy              ⁡                              (                                                      13                    ⁢                                          x                      2                                                        +                                      15                    ⁢                                          y                      2                                                        +                                      6                    ⁢                                          z                      2                                                                      )                                                          8            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                    ⁢                                  -                                                            35                π                                      ⁢                          x              ⁡                              (                                                      x                    2                                    -                                      3                    ⁢                                          y                      2                                                                      )                                      ⁢            z                                8            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                                        Equation        ⁢                                  ⁢        L        ⁢                                  ⁢                  -                ⁢                                  ⁢        Column        ⁢                                  ⁢        12                                                      5            ⁢                                          3                                  7                  ⁢                  π                                                      ⁢                          xy              ⁡                              (                                                      x                    2                                    +                                      y                    2                                    -                                      6                    ⁢                                          z                      2                                                                      )                                                          8            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                    ⁢                                  ⁢                                                                                                                        3                                              7                        ⁢                        π                                                                              ⁢                                      (                                                                  -                                                  x                          4                                                                    +                                              3                        ⁢                                                  (                                                                                    y                              2                                                        +                                                          z                              2                                                                                )                                                ⁢                                                  x                          2                                                                    +                                                                                                                                                                                      4                      ⁢                                              y                        4                                                              +                                          4                      ⁢                                              z                        4                                                              -                                          27                      ⁢                                              y                        2                                            ⁢                                              z                        2                                                                              )                                                                          8            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                    ⁢                                  ⁢                              5            ⁢                                          3                                  7                  ⁢                  π                                                      ⁢                          yz              ⁡                              (                                                      3                    ⁢                                          (                                                                        x                          2                                                +                                                  y                          2                                                                    )                                                        -                                      4                    ⁢                                          z                      2                                                                      )                                                          8            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                                        Equation        ⁢                                  ⁢        M        ⁢                                  ⁢                  -                ⁢                                  ⁢        Column        ⁢                                  ⁢        13                                          -                                                                      15                                      14                    ⁢                    π                                                              ⁢              yz              ⁢                              (                                                                            -                      6                                        ⁢                                          x                      2                                                        +                                      y                    2                                    +                                      z                    2                                                  )                                                    2              ⁢                                                (                                                            x                      2                                        +                                          y                      2                                        +                                          z                      2                                                        )                                                  9                  /                  2                                                                    ⁢                                  -                                                            15                                  14                  ⁢                  π                                                      ⁢                          xz              ⁡                              (                                                      x                    2                                    -                                      6                    ⁢                                          y                      2                                                        +                                      z                    2                                                  )                                                          2            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                    ⁢                                  -                                                            15                                  14                  ⁢                  π                                                      ⁢                          xy              ⁡                              (                                                      x                    2                                    +                                      y                    2                                    -                                      6                    ⁢                                          z                      2                                                                      )                                                          2            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                                        Equation        ⁢                                  ⁢        N        ⁢                                  ⁢                  -                ⁢                                  ⁢        Column        ⁢                                  ⁢        14                                                                                    5                                  7                  ⁢                  π                                                      ⁢                          xy              ⁡                              (                                                                            -                      15                                        ⁢                                          x                      2                                                        +                                      13                    ⁢                                          y                      2                                                        +                                      6                    ⁢                                          z                      2                                                                      )                                                          8            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                    ⁢                                  ⁢                                                                                                                        5                                              7                        ⁢                        π                                                                              ⁢                                      (                                                                  3                        ⁢                                                  x                          4                                                                    +                                              3                        ⁢                                                  (                                                                                    z                              2                                                        -                                                                                                                                                                                                                                                                                                                7                          ⁢                                                      y                            2                                                                          )                                            ⁢                                              x                        2                                                              +                                          4                      ⁢                                              y                        4                                                              -                                          3                      ⁢                                              y                        2                                            ⁢                                              z                        2                                                                              )                                                                          8            ⁢                                          (                                                      x                    2                                    +                                      y                    2                                    +                                      z                    2                                                  )                                            9                /                2                                                    ⁢                                  ⁢                                                                              35                  π                                            ⁢                              y                ⁡                                  (                                                            y                      2                                        -                                          3                      ⁢                                              x                        2                                                                              )                                            ⁢              z                                      8              ⁢                                                (                                                            x                      2                                        +                                          y                      2                                        +                                          z                      2                                                        )                                                  9                  /                  2                                                              .                                    Equation        ⁢                                  ⁢        O        ⁢                                  ⁢                  -                ⁢                                  ⁢        Column        ⁢                                  ⁢        15            